Deep Learning Quantum States for Hamiltonian Estimation

Human experts cannot efficiently access the physical information of quantum many-body states by simply "reading" coefficients, but have to reply on previous knowledge such as order parameters and measurements. In this work, we demonstrate that convolutional neural network (CNN) can learn from coefficients local reduced density matrices estimate Hamiltonians, coupling strengths magnetic fields, provided ground states. We propose QubismNet consists two main parts: Qubism map visualizes (or purified matrices) images, a CNN maps images target parameters. By assuming certain constraints training set for sake balance, exhibits impressive powers learning generalization several spin models. While samples are restricted ranges parameters, accurately beyond regions. For instance, our results show fields near critical point away vicinity. Our work illuminates data-driven way infer Hamiltonians give designed states, therefore would benefit existing future generalizations technologies Hamiltonian-based simulations state tomography.